Piezoelectric resonant-based mechanical frequency combs

ABSTRACT

The present disclosure describes systems and methods for novel phononic frequency combs and related sensing techniques realized by a piezoelectric multimode or single-mode mechanical resonator based on parametric pumping. In one embodiment of such a system, a single frequency electrical input provides an electrical signal comprising an amplitude and a single input frequency to a multimode mechanical resonator, in which a value of the single input frequency equals a sum of the resonance frequencies of the two resonance modes of the mechanical resonator. Accordingly, the mechanical resonator is configured to produce at least one phononic frequency comb in response to a motion of the mechanical resonator caused by the electrical signal.

CROSS-REFERENCE TO RELATED APPLICATION

This application is the 35 U.S.C. § 371 national stage application ofPCT Application No. PCT/US19/31504, filed May 9, 2019, which claimspriority to U.S. provisional application entitled, “PiezoelectricResonant-Based Micromechanical Frequency Combs,” having Ser. No.62/669,143, filed May 9, 2018, all of which are entirely incorporatedherein by reference.

TECHNICAL FIELD

The present disclosure is generally related to micromechanical frequencycombs.

BACKGROUND

Frequency combs have been used in frequency synthesizers, precision timemetrology, and molecular spectroscopy as well as wavelengthmultiplexing. While optical frequency combs haven been widely usedpreviously, their micromechanical counterparts have only been recentlydemonstrated by electrostatic coupling of two or more resonators ormultiple input frequencies.

Other techniques for micromechanical frequency combs are contemplated inthis disclosure that are new and novel, including tunablemicromechanical frequency combs with electrical input and output, whichoperate based on a single electrical tone frequency with low inputpower.

SUMMARY

Embodiments of the present disclosure provide systems and methods forphononic frequency combs and related sensing techniques realized by apiezoelectric multimode or single-mode mechanical resonator based onparametric pumping. Briefly described, one embodiment of the system,among others, can be implemented as follows. A single frequencyelectrical input (pump) provides an electrical signal comprising anamplitude and a single input frequency to a multimode mechanicalresonator. The mechanical resonator is configured to produce at leastone phononic frequency comb in response to a motion of the mechanicalresonator caused by the electrical signal. Accordingly, the mechanicalresonator comprises a piezoelectric structure having two resonance modeswithin a single acoustic cavity of the mechanical resonator, coupled bythin film stress; and a value of the single input frequency equals a sumof the resonance frequencies of the two resonance modes of themechanical resonator which is referred as non-degenerate parametricpumping.

Other embodiments having additional features are also disclosed. Suchfeatures include wherein three sets of frequency combs are achieved,wherein two sets are located proximal to the two resonance modes of themechanical resonator and one set is located at the single inputfrequency, wherein each of the frequency combs have equally-distancedspectral lines; wherein a frequency spacing of the phononic frequencycomb is selectively adjustable based on the electrical signal of thesingle frequency electrical input; wherein the frequency and theamplitude of the electrical signal are selective adjustable; wherein themechanical resonator comprises a piezoelectric circular drumheadresonator; wherein the piezoelectric circular drumhead resonatorcomprises an AlN-on-Si circular membrane surrounded by a mesa structure;and wherein the resonance modes of the mechanical resonator are tunableby applying a DC voltage to a clamped boundary of the mechanicalresonator, or by adjusting the amplitude and frequency, among otherpossible features. Possible applications for the disclosed phononicfrequency comb systems include a self-sustained micromechanical sensorand a frequency synthesizer, among others.

The present disclosure also provides phononic frequency comb methods. Inthis regard, one embodiment of such a method, among others, can bebroadly summarized by the following: coupling a multimode mechanicalresonator with a single frequency electrical input; driving themechanical resonator with an electrical signal generated by the pumpdevice, the electrical signal having an amplitude and a single inputfrequency; producing at least one phononic frequency comb in response toa motion of the mechanical resonator caused by the electrical signal;and probing the mechanical resonator to output a signal comprising theat least one phononic frequency comb; wherein the mechanical resonatorcomprises a piezoelectric structure having two resonance modes within asingle acoustic cavity of the mechanical resonator; and wherein a valueof the single input frequency equals a sum of the resonance frequenciesof two acoustic modes of the mechanical resonator.

Other embodiments having additional operations and features are alsodisclosed. Such operations and/or features may include wherein the atleast one phononic frequency comb comprises three sets of frequencycombs, wherein two sets are located proximal to the two resonance modesof the mechanical resonator and one set is located at the single inputfrequency, wherein each of the frequency combs has equally-distancedspectral lines; adjusting a frequency spacing of the phononic frequencycomb based on the electrical signal of the single frequency electricalinput device; wherein the frequency and the amplitude of the electricalsignal are selective adjustable; wherein the mechanical resonatorcomprises a piezoelectric circular drumhead resonator; wherein thepiezoelectric circular drumhead resonator comprises an AlN-on-Sicircular membrane surrounded by a mesa structure; wherein a diameter ofthe circular drumhead resonator does not exceed 30 μm; tuning theresonance modes of the mechanical resonator by applying a DC voltage toa clamped boundary of the mechanical resonator; detecting perturbationsin the environment utilizing the at least one phononic frequency comb;and/or synthesizing a range of frequencies based on the at least onephononic frequency comb.

Other systems, methods, features, and advantages of the presentdisclosure will be or become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such additional systems, methods, features, andadvantages be included within this description.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the present disclosure can be better understood withreference to the following drawings. The components in the drawings arenot necessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1A is a block diagram of an exemplary phononic frequency combsystem in accordance with various embodiments of the present disclosure.

FIG. 1B is a diagram showing a resonant frequency shift of the drivenmodes of an exemplary phononic frequency comb sensing scheme inaccordance with various embodiments of the present disclosure.

FIG. 1C is a diagram showing the creation of phononic frequency combsclose to two mechanical modes of an exemplary phononic frequency combsensing scheme in accordance with various embodiments of the presentdisclosure.

FIG. 2A is a scanning electronic micrograph (SEM) image of an AlN-on-Simechanical resonator for an exemplary phononic frequency comb sensor inaccordance with various embodiments of the present disclosure.

FIG. 2B is a diagram showing a cross section view of the AlN-on-Simechanical resonator of FIG. 2A.

FIG. 3A is a diagram of a driven resonance mode along with displace modeshape at different input power levels for a first mechanical mode(mode 1) of an exemplary mechanical resonator of a phononic frequencycomb sensor in accordance with various embodiments of the presentdisclosure.

FIG. 3B is a diagram of a driven resonance mode along with displace modeshape at different input power levels for a second mechanical mode (mode2) of an exemplary mechanical resonator of a phononic frequency combsensor in accordance with various embodiments of the present disclosure.

FIG. 4 is a diagram showing an exemplary phononic frequency combspectrum centered at an idler frequency with spacing determined by thedetuning of the pump from the sum of mechanical modes.

FIG. 5 is a diagram illustrating a single tone that can be applied toexcite the signal and idler mode with a frequency offset for a phononicfrequency comb sensor in accordance with various embodiments of thepresent disclosure.

FIG. 6A shows the device geometry and displacement mode shapes of twomechanical resonance modes of an exemplary mechanical resonator of aphononic frequency comb sensor in accordance with various embodiments ofthe present disclosure.

FIG. 6B shows an exemplary comb measurement scheme highlighting thetuning of center frequencies and frequency spacings of two sets offrequency combs located close to the mechanical resonance modes of anexemplary mechanical resonator of a phononic frequency comb sensor bydetuning the pump frequency and power in accordance with variousembodiments of the present disclosure.

FIG. 6C provides a plot of the frequency of signal and idler as the pumpfrequency is swept for an exemplary phononic frequency comb inaccordance with embodiments of the present disclosure.

FIG. 6D is a plot of the frequency of signal and idler as static stressinduced by DC voltage is swept for an exemplary phononic frequency combin accordance with embodiments of the present disclosure.

FIG. 7 is a plot demonstrating the frequency tuning of the twomechanical modes versus DC voltage for an exemplary phononic frequencycomb in accordance with embodiments of the present disclosure.

FIGS. 8A-8D show different dynamical regimes depicting the sequentialevolution of the power spectrum as the parametric pump frequencyincreases for an exemplary phononic frequency comb in accordance withvarious embodiments of the present disclosure.

FIG. 9 is a flow chart diagram illustrating an exemplary phonicfrequency comb method in accordance with various embodiments of thepresent disclosure.

DETAILED DESCRIPTION

The present disclosure describes systems and methods for novel phononicfrequency combs and related sensing techniques realized by apiezoelectric multimode mechanical resonator (e.g., micromechanical ornanomechanical piezoelectric resonator) based on parametric pumping. Inone embodiment, an integrated, self-sustained, high-Quality (Q),resonant-based frequency comb sensor is used as a sensor to track thefrequency spacing between spectral lines of the frequency comb in orderto increase the sensor sensitivity and cancel out the environmentaldrift effects on the sensor responsivity.

While mechanical resonators, in the most general definition, are passivecomponents which are integrated with an energy restoring element (e.g.an electronic amplifier) to sustain oscillation in a feedback-loopsystem, embodiments of the present disclosure utilize a single frequencyelectrical input (e.g., a single tone pump device such as an AC voltagesource) with an input or pump frequency equal to the sum of thefrequencies of two acoustic or mechanical resonance modes within thesame mechanical resonator Other embodiments utilize a single frequencyelectrical input with an input frequency equal to twice the resonancemode of a single-mode mechanical resonator.

Referring now to FIG. 1A, a block diagram of an exemplary phononicfrequency comb system 100 of an embodiment of the present disclosure isdepicted. In the figure, an electrical AC signal, from a single tonepump device 110 (also referred as a single frequency electrical input),drives a multimode piezoelectric mechanical resonator 120. The pumpfrequency (also referred as an input frequency) of the electrical signalis equal to the sum of the frequencies of two mechanical or acousticmodes of the mechanical resonator 120. Further, by applying a signalfrom a DC voltage source 130 coupled to the multimode mechanicalresonator 120, the mechanical modes of the mechanical resonator 120 canbe adjusted. The mechanical resonator 120 is configured to produce atleast one phononic frequency comb at an output 140 in response to amotion of the mechanical resonator caused by the electrical signal.

In one embodiment, the mechanical resonator 120 comprises apiezoelectric structure having two resonance modes within a singleacoustic cavity of the mechanical resonator. In one embodiment, aplurality of phononic frequency combs can be obtained by probing anoutput 150 of the mechanical resonator 120. For example, the output mayinclude phononic frequency combs comprising three sets of frequencycombs, wherein two sets are located proximal to the two resonantmechanical modes of the mechanical resonator and one set is located atthe pump frequency, each of the frequency combs having equally-distancedphase-coherent spectral lines. In various embodiments, the frequencyspacing of the phononic frequency comb(s) are selectively adjustablebased on the electrical signal of the pump device 110.

The disclosed techniques offer several advantages over traditionalMEMS-CMOS oscillator counterparts. First, they obviate the need forelectronic circuitry (e.g., electronic amplifier) that suffers from shotnoise overcoming the associated challenges with MEMS-CMOS integration,and thus improve the overall noise performance. Second, they offer asmaller footprint that takes advantage of piezoelectric-induced modecoupling between two (or more) resonance modes within the same acousticcavity and a single tone pump 110.

Accordingly, the present disclosure provides embodiments for phononicfrequency comb systems and methods based on efficient simultaneousexcitation of two resonance modes using a single tone pump 110. Toillustrate, an exemplary embodiment involves the generation and tuningof phononic frequency combs in a fully-integrated standalonepiezoelectric platform. In practice, such frequency combs can be usedfor high-precision sensing that tracks frequency spacing between thephase-coherent spectral lines as the analogue of “beat frequency” indual-mode oscillators.

For the single tone pump device 110, its pump frequency can be detunedfrom (f_(m1)+f_(m2)), where f_(m1) and f_(m2) are the two mechanicalmodes of the mechanical resonator, such that the pump frequency inducesan idler and signal mode at frequencies close to f_(m1) and f_(m2).Frequency mixing between the idler (signal) mode and f_(m1) (f_(m2)) maythen create Δf₁ (Δf₂) that are proportional to the detuning of the pump110 from f_(m1)+f_(m2). Such a scheme can significantly reduce theelectronics required for multipliers and mixers used in dual-modeoscillators to track “beat frequency.”

In accordance with the present disclosure, any two mechanical modes canbe chosen to generate frequency combs based on non-degenerate parametricpumping, in which the threshold power for comb generation can be reducedby designing high Q-resonance modes with high coupling rates.Furthermore, by utilizing two modes with different sensitivities, onecan decrease the frequency shift through their linear combination.

Referring now to the figures, FIG. 1B and FIG. 1C show an exemplarynovel phononic frequency comb scheme in accordance with variousembodiments of the present disclosure. In FIG. 1B, a resonant frequencyshift of the driven modes of an embodiment of phononic frequency combsis presented. The resonant frequency shifts are due to a change in theeffective mass or stiffness of the mechanical resonator. An applied DCvoltage changes the stiffness of the mechanical resonator with differentsensitivities at mode 1 and 2. In this example, the DC voltage is variedfrom −0.1 V to 0.1 V in 0.1 V steps and sensitivities of 0.015 N and0.022 N are observed for the two resonance modes. Next, in FIG. 1C, thecreation of frequency combs 200 close to two mechanical modes of themechanical resonator is depicted for an exemplary embodiment of thepresent disclosure. As the DC voltage changes the stress, the detuningfrequency between the pump 110 and the sum of the two mechanical modeschange. Here, the two mechanical modes undergo different frequencyshifts as the stiffness of a circular membrane of a mechanicalresonator, in one embodiment, is modulated by DC voltage (from −0.1 V to0.1 V with 0.1 V steps). The shift in the mechanical modes cause a shiftin the detuned frequency and thus a change in the frequency spacing ofthe frequency comb 200.

In one embodiment, the frequency spacing between spectral lines aregenerated based on four-wave mixing between two resonance modes and pumpfrequency. Further, the center frequency and frequency spacing can beadjusted by tuning the frequency and the power (amplitude) of pump tone.Moreover, the frequencies of two mechanical modes can be tuned byapplication of a DC voltage and modulation of piezoelectrically-inducedstress (thin film stress).

Referring now to FIG. 2A, the figure shows a scanning electronmicrograph (SEM) image of an embodiment of a circular membrane 210 ofthe mechanical resonator 120 (e.g., a piezoelectric circular drumheadresonator). In particular, a measurement setup for frequency combgeneration is depicted utilizing a fabricated AlN-on-Si circularmembrane surrounded by a mesa structure, where Aluminum Nitride (AlN) isa piezoelectric material. A single tone pump 110 drives the mechanicalresonator 120 and the output probe 140 (e.g., via a spectrum analyzer)probes the motion of the resonator to generate an output signal having afrequency comb pattern. In this exemplary embodiment, the radius of thecircular membrane is, but not limited, to 15 μm. The mechanicalresonator structure also includes gold contacts, release holes in thecircular membrane 210 for isotopically etching a buried oxide layer withhydrofluoric acid (HF), and top and bottom electrodes comprisingmolybdenum (Mo). In certain embodiments, a bias-T circuit component 220may also be used to couple a DC voltage 130 to the mechanical resonator120 (which can induce thin film stress and shift a resonance frequencyof the resonator 120).

Correspondingly, FIG. 2B demonstrates an exemplary cross section of theresonant stack for the mechanical resonator 120 (of FIG. 2A) with atotal of <200 nm thickness for various embodiments. Such a thin membranehelps achieve nonlinear behavior at lower power levels. As shown in thefigure, an embodiment of such a thin membrane includes a piezoelectricstack having layers of Mo (25 nm), AlN (50 nm), and Mo (50 nm) on aSilicon on Insulin wafer having layers of AlN (20 nm), Si (50 nm), SiO₂(2 μm), and Si (500 μm). When the multimode mechanical resonator 120 ispumped with a single tone at a frequency close to the sum of twomechanical modes (f_(m1)+f_(m2)), a frequency comb 200 is generatedclose to each of the mechanical modes having a set of equally-distancedphase-coherent spectral lines.

In one exemplary embodiment, a generated frequency comb 200 has a centerfrequency of 3.548 MHz with a frequency spacing of 404 Hz. However, thecenter frequency and frequency spacing of the comb can be adjusted bytuning the pump frequency and amplitude. Furthermore, due to themechanical mode frequencies being very sensitive to DC voltage, themodes can be tuned by static piezoelectric stress (thin film stress).For example, with respect to FIGS. 2A and 2B, the large nonlinearitypresent in the stiffness of thin AlN films causes the amplitude of oneresonance mode to shift the resonance frequency of another mode. Thethin film stress-induced coupling between the two mechanical modes isdetermined by the displacement amplitude, dissipation rate, resonancefrequency and mode shapes of each mode induced by the piezoelectricexcitation. Therefore, by taking advantage of the mode coupling betweentwo modes in the same acoustic cavity of the mechanical resonator 120,the size of the frequency comb can be made minimal. To illustrate, oneembodiment of a piezoelectric frequency comb in accordance with thepresent disclosure only has a 30 μm×30 μm footprint and features alinear center frequency tuning capability by pump frequency.

Further details of embodiments of the phononic frequency comb areprovided in the following figures and accompanying descriptions.Accordingly, FIGS. 3A and 3B show the driven resonance modes of the twoacoustic resonance modes of the mechanical resonator 120 at differentinput power levels, demonstrating the Duffing nonlinearity. Thegoverning harmonic oscillator equations that include the two coupledmodes are:

{umlaut over (x)} ₁+ω₁ ² x ₁+(w ₁ /Q ₁){dot over (x)} ₁+(y ₁₂ /m ₁)x ₁ x₂ ²+(α₁ /m ₁)x ₁ ³=(F/m ₁)x ₂ cos ω_(p) t  (1)

{umlaut over (x)} ₂+ω₂ ² x ₂+(w ₂ /Q ₂){dot over (x)} ₁+(y ₂₁ /m ₂)x ₂ x₁ ²+(α₂ /m ₂)x ₂ ³=(F/m ₂)x ₁ cos ω_(p) t  (2)

where x_(1,2) are the mode displacements, Q_(1,2) are the Q factors,m_(1,2) are the effective masses, ω_(1,2) are the Duffing nonlinearitycoefficients for mode 1 and 2 respectively, y₁₂ denotes the dispersivecoupling between mode 1 and 2; ω_(p) is the pump frequency; and F is theamplitude of the pump 110.

Next, FIG. 4 presents an exemplary phononic frequency comb spectrumcentered at the idler frequency (3.548 MHz) with spacing determined bythe detuning of the pump 110 from the sum of the frequencies for themechanical modes. Here, a shift in frequency spacing, due to an appliedDC voltage 130, shifts the frequencies for the two mechanical modes. Asdemonstrated in FIG. 5, a single tone at f_(p), detuned fromf_(m1)+f_(m2), can be applied to excite the signal and idler mode with afrequency offset of Δf₁ and Δf₂, where f_(m1) and f_(m2) correspond tothe u₀₁ and u₁₁ modes (first mechanical mode and the second mechanicalmode) shown in FIG. 3A and FIG. 3B. The single tone at f_(p) (i.e.,ω_(p)/2π) induces a signal and idler distanced by Δf₁ and Δf₂ fromf_(m1) and f_(m2) respectively.

In FIG. 6A, the comb generation using non-degenerate parametric pumpfrequency at the sum of the two mechanical modes, corresponding to u₀₁and u₁₁ is depicted. Here, the sets of combs are observed with two setsbeing placed close to the signal/idler frequency and one centered at thepump frequency. On the top right of the figure, a SEM image of astandalone AlN-on-Si micromechanical resonator is shown. For FIG. 6B, bytuning the pump amplitude and frequency, the figure illustrates that thecenter frequency of combs and Δf_(p) can be detuned. At FIG. 6C, thesignal and idler frequencies are plotted as the pump frequency is sweptshowing a linear trend. In addition, the plot shows that tuning thecenter frequency of the phononic comb is possible by tuning the pumpfrequency. Furthermore, the mechanical resonance modes can be tuned bystatic piezoelectric stress induced by DC voltage at clamped boundariesof the mechanical resonator 120, as shown by FIG. 6D. For example, FIG.7 demonstrates the frequency tuning of the two mechanical modes versusDC voltage for an exemplary embodiment. It is observed in this examplethat the frequency spacing is 404 Hz at a pump frequency of 8.77 MHz,where the input pump power was maintained at 30 dBm.

In FIGS. 8A-8D, four different dynamic states of parametric excitationclose to mechanical resonance modes of a drumhead circular MEM resonatorare investigated. In particular, FIGS. 8A-8D depict the continuoussequel of parametric excitation in a strongly driven nonlinear MEMresonator. At a constant pump power of 7 dBm, the pump frequency isswept with 2 kHz steps, starting at 8.828 MHz, where no signal/idlertone is observed. The spectrum evolves into formation of a single tone(signal/idler), combs, and chaotic behavior. Accordingly, differentdynamical regimes depicting the sequential evolution of the powerspectrum as the parametric pump frequency increases from FIG. 8A to FIG.8D are provided. The four different dynamic states are described below.

For State 1, there is no parametric excitation and marks the beginningand end of the evolution sequence, as shown in FIG. 8A. For State 2, asingle tone is generated close to u₁₁ resonance mode of the circularmembrane, as shown in FIG. 8B. This state exists at pump frequenciesranging from 8.83 MHz to 8.902 MHz. For State 3, the tone breaks downinto several equidistanced spectral lines (frequency combs), as shown inFIG. 8C, with the pump frequency ranging from 8.904 MHz to 8.916 MHz,resembling the spectrum of temporal solitary waves in optomechanicalsystems. For State 4, a triangular-envelope spectrum persists for afrequency range of 106 kHz bandwidth from 8.918 MHz to 9.024 MHz, asshown in FIG. 8D.

In an alternative embodiment, instead of non-degenerate parametricpumping, degenerate parametric pumping may be used such that frequencycombs can be achieved with a single resonance mode, when the pumpfrequency is twice the frequency of the resonance mode. As a result, aset of frequency combs can be achieved with a center frequency close tothe resonance mode of the resonator.

In summary, instead of using external coupling mechanisms of two or moreresonators, as demonstrated by earlier techniques, embodiments of thepresent disclosure take advantage of piezoelectric stress-induced modecoupling within the same acoustic cavity of a multimode mechanicalresonator 120. Certain embodiments of a phononic frequency comb 200 inaccordance with the present disclosure utilizes non-degenerateparametric pumping to induce a signal and idler mode close to twomechanical modes of a mechanical resonator 120 and uses frequency mixingand subharmonic excitation inherent to the nonlinear behavior of themechanical resonator 120 to generate multiple spectral lines (e.g., witha frequency spacing of ˜404 Hz), which provides several advantages overearlier techniques. For example, an advantage over degenerate parametricexcitation lies in the fact that the two mechanical modes can bearbitrarily designed and chosen, wherein the added degree of freedomallow for accurate control over the frequency spacing between thespectral lines and the center frequency. Moreover, phononic frequencycombs of the present disclosure have applications, among others, ashighly sensitive dual-mode sensors, self-sustained micromechanicalsensors, and/or frequency synthesizers that can be optimized to cancelout environmental drifts with enhanced “beat frequency,” while takingadvantage of its simplified design and small size.

Another advantage is the phase coherence of the spectral lines of phonicfrequency combs of various embodiments of the present disclosure. Forexample, the generated side bands (at the sum of two mechanical modes(f_(m1)+f_(m2))) have a defined phase relationship with respect to thepump phase. In contrast, for many conventional phononic techniques, thefrequency-shift detection is often not limited by the resonator Q, butinstead bound to some anomalous temperature-dependent frequency/phasefluctuations. Additionally, oscillator circuits traditionally have phasefreedom, while their amplitude arc is limited by a limiting amplifier ora nonlinearities in the system. Thus, using a phase coherent detectionmechanism along with two-mode compensation techniques, in accordancewith the present disclosure, will yield higher phase stability ascompared to traditional amplitude-saturated oscillator circuits.Accordingly, embodiments of the phononic frequency comb of the presentdisclosure can replace traditional MEMS-CMOS integrated configuration asthe building block of oscillators, which can decrease the footprint andthe noise (e.g., shot noise) associated with electronic circuitry. Forexample, by taking advantage of two resonance modes within the sameacoustic cavity, the electronic design can be significantly simplified.

To illustrate, an exemplary phononic frequency comb of the presentdisclosure, is in principle, analogous to the optical micro-resonatorfrequency combs which are widely used in frequency synthesizers anddual-mode sensing applications. However, unlike the optical frequencycomb counterparts, an exemplary phononic frequency comb isfully-integrated, with voltage input and output, does not requirecoupling of light to a micro-resonator and relies on optimizing thedesign of a single acoustic cavity instead of optical and acousticcavity optimization.

While traditional techniques utilize an energy restoring element thatcompensates for the losses in the mechanical resonator in a feedbackloop, an exemplary embodiment of a phononic frequency comb of thepresent disclosure does not require such an energy restoring element byutilizing a single tone pump 110 with a frequency equal to the sum ofthe frequencies of two acoustic modes within a single mechanicalresonator 120. Accordingly, embodiments of the present disclosure arewell-suited for many applications, such as synthesizing a range offrequencies based on the at least one phononic frequency comb. Otherapplications also include detecting perturbations in the environment(e.g., a change in temperature or mass associated with the mechanicalresonator), since resonant frequency-shift detection has proven to be ahighly accurate sensing method.

Referring to FIG. 9, shown is a flow chart 800 illustrating an exemplaryphonic frequency comb method in accordance with embodiments of thepresent disclosure. Beginning with 810, a multimode mechanical resonator120 is coupled with a single tone pump device 110. Next, the mechanicalresonator 120 is driven with an electrical signal generated (820) by thepump device 110 in which the electrical signal has a pump amplitude anda single pump frequency, wherein a value of the pump frequency equals asum of the resonance frequencies of two acoustic or mechanical resonancemodes of the mechanical resonator 120. In response to a motion of themechanical resonator 120 caused by the electrical signal, at least onephononic frequency comb is produced (830). Therefore, the mechanicalresonator 120 can be probed (840) to extract an output signal from anelectrode of the mechanical resonator 120, where the signal comprisesthe at least one phononic frequency comb. In various embodiments,additional operations may include adjusting a frequency spacing of thephononic frequency comb based on the electrical signal of the pumpdevice and/or tuning the resonance modes of the mechanical resonator byapplying a DC voltage to a clamped boundary of the mechanical resonator,among others.

It should be emphasized that the above-described embodiments of thepresent disclosure are merely possible examples of implementations,merely set forth for a clear understanding of the principles of thedisclosure. Many variations and modifications may be made to theabove-described embodiment(s) without departing substantially from theprinciples of the present disclosure. All such modifications andvariations are intended to be included herein within the scope of thisdisclosure and the following claims.

1. A phonic frequency comb system comprising: a single frequencyelectrical input to provide an electrical signal comprising an amplitudeand a single input frequency; a multimode mechanical resonator toreceive the electrical signal, the multimode mechanical resonatorconfigured to produce at least one phononic frequency comb in responseto a motion of the multimode mechanical resonator caused by theelectrical signal; and wherein the multimode mechanical resonatorcomprises a piezoelectric structure having two resonance modes within asingle acoustic cavity of the multimode mechanical resonator coupled bythin film stress; and wherein a value of the single input frequencyequals a sum of resonance frequencies of two resonance modes of themultimode mechanical resonator.
 2. The system of claim 1, wherein the atleast one phononic frequency comb comprises three sets of frequencycombs, wherein two sets are located proximal to the two resonance modesof the multimode mechanical resonator and one set is located at thesingle input frequency, each of the frequency combs havingequally-distanced spectral lines.
 3. The system of claim 1, wherein afrequency spacing of the at least one phononic frequency comb isselectively adjustable based on the electrical signal of the singlefrequency electrical input.
 4. The system of claim 1, wherein the singleinput frequency and the amplitude of the electrical signal are selectiveadjustable.
 5. The system of claim 1, wherein the multimode mechanicalresonator comprises a piezoelectric circular drumhead resonator.
 6. Thesystem of claim 5, wherein the piezoelectric circular drumhead resonatorcomprises an AlN-on-Si circular membrane surrounded by a mesa structure.7. The system of claim 5, wherein a diameter of the piezoelectriccircular drumhead resonator does not exceed 30 μm.
 8. The system ofclaim 1, wherein the resonance modes of the multimode mechanicalresonator are tunable by applying a DC voltage to a clamped boundary ofthe multimode mechanical resonator.
 9. A self-sustained micromechanicalsensor comprising the system of claim
 1. 10. A phonic frequency combmethod comprising: coupling a multimode mechanical resonator with asingle frequency electrical input; driving the multimode mechanicalresonator with an electrical signal generated by the single frequencyelectrical input, the electrical signal having an amplitude and a singleinput frequency; producing at least one phononic frequency comb inresponse to a motion of the multimode mechanical resonator caused by theelectrical signal; and probing the multimode mechanical resonator tooutput a signal comprising the at least one phononic frequency comb;wherein the multimode mechanical resonator comprises a piezoelectricstructure having two resonance modes within a single acoustic cavity ofthe multimode mechanical resonator; and wherein a value of the singleinput frequency equals a sum of resonance frequencies of two acousticmodes of the multimode mechanical resonator.
 11. The method of claim 10,wherein the at least one phononic frequency comb comprises three sets offrequency combs, wherein two sets are located proximal to the tworesonance modes of the multimode mechanical resonator and one set islocated at the single input frequency, each of the frequency combshaving equally-distanced spectral lines.
 12. The method of claim 10,further comprising adjusting a frequency spacing of the phononicfrequency comb based on the electrical signal of the single inputelectrical input.
 13. The method of claim 12, wherein the frequency andthe amplitude of the electrical signal are selective adjustable.
 14. Themethod of claim 10, wherein the multimode mechanical resonator comprisesa piezoelectric circular drumhead resonator.
 15. The method of claim 14,wherein the piezoelectric circular drumhead resonator comprises anAlN-on-Si circular membrane surrounded by a mesa structure.
 16. Themethod of claim 14, wherein a diameter of the piezoelectric circulardrumhead resonator does not exceed 30 μm.
 17. The method of claim 10,further comprising tuning the resonance modes of the multimodemechanical resonator by applying a DC voltage to a clamped boundary ofthe multimode mechanical resonator.
 18. The method of claim 10, furthercomprising detecting perturbations in an environment utilizing the atleast one phononic frequency comb.
 19. The method of claim 10, furthercomprising synthesizing a range of frequencies based on the at least onephononic frequency comb.
 20. A phonic frequency comb system comprising:a single frequency electrical input to provide an electrical signalcomprising an amplitude and a single input frequency; a single-modemechanical resonator to receive the electrical signal, the single-modemechanical resonator configured to produce at least one phononicfrequency comb in response to a motion of the single-mode mechanicalresonator caused by the electrical signal; wherein the single-modemechanical resonator comprises a piezoelectric structure having aresonance mode within a single acoustic cavity of the single-modemechanical resonator coupled by thin film stress; and wherein a value ofthe single input frequency equals twice a value of the resonance mode ofthe single-mode mechanical resonator.